The process of detecting and characterizing a specific portion of a region to be imaged has increasingly been used in the treatment of information on images associated with various disciplines such as medicine, biomedicine, nuclear physics, satellite imaging, non-destructive inspection (NDI) and other imaging fields. Considerable effort has been expended to enhance the contrast of an image with respect to two distinct domains of a region of interest that are physically close and have similar signal characteristics.
In non-destructive inspections, the aim of an efficient imaging technology is to ascertain the presence and the location of small flaws in the material to be inspected. Imaging technologies have also become extremely valuable in the medical field and have proven to be quite effective in the field of medical diagnosis. In particular, computed tomography (CT X-ray scans) and Magnetic Resonance Imaging (MRI) are used extensively in medical imaging for generating high quality images of the body. In medical imaging, a frequent objective is to distinguish normal from abnormal tissue, for example a tumor growth on an organ. This presents a very difficult imaging problem in at three respects. First, the signals representative of the abnormal tumor cells are often quite similar to the signals representative of the normal cells of the organ. Second, since it is desirable to detect such abnormal growths as early as possible, the total volume or number of abnormal cells, is much smaller than the total volume or number of normal cells. Third, the abnormal cells are immediately adjacent to or in close proximity to the normal cells.
In most imaging techniques, and in particular medical imaging, the region of interest, i.e., the region of the object being imaged, is typically partitioned into a plurality of volume elements called voxels. A signal derived from the imaging technology (e.g. an X-ray signal in CT or an NMR signal in MRI) is averaged over each individual volume element or voxel. The composite of these averaged signals for all of the voxels comprising the region of interest form a representation of the object being imaged in signal space. These signals indirectly correspond to physical and/or chemical characteristics of the materials comprising the voxels being imaged. The properties of the materials within the region of interest directly affect the signals corresponding to their respective voxel elements. The manner in which the signals are affected is, of course, dependent upon the particular phenomenon, i.e., X-ray, NMR, etc., involved in the imaging technique. The signals may comprise a single component or a plurality of components. If the signals consist of a single component, as in computed tomography, they form a scalar field. If the signals comprise more than one component, as in MRI, the signal from each voxel can be characterized as a signal vector in a signal space having a dimension equal to the number of components comprising each signal vector. In magnetic resonance imaging, three components of interest are typically selected to describe the characteristics of the region of interest being imaged. These components are the spin-lattice relaxation time T.sub.1, the spin-spin relaxation time T.sub.2, and a spin density for hydrogen. The components of the signal vectors are assumed to form a set of basis vectors which span the signal space for all regions of interest within the object being inspected. This assumption is not always true since the individual components of the signals are often correlated, i.e., not independent. For instance, in magnetic resonance imaging, the proton density is related to the values of the times of relaxation T.sub.1 and T.sub.2. An increase in water content not only increases the hydrogen density and hence the proton density, but it also increases the times of relaxation, T.sub.1 and T.sub.2. The proton density and relaxation times T.sub.1 and T.sub.2 do, however, form a good approximation to a basis for a three dimensional signal space. Thus, the signal from a voxel within the region of interest is mapped into a 3-dimensional vector in the signal space. The magnitude and direction of each vector is determined by the intensity of the signals corresponding to each of the three components. Other components may also be considered in MRI, such as microscopic diffusion and microscopic rotational states of the resonant nuclei.
An image corresponding to the signal values of the voxels can be displayed, for example, on a standard CRT in digital format. The image is partitioned into a set of picture elements called pixels, there being a one-to-one correspondence between the voxels of the region of interest to be imaged and between the pixels of the displayed image. The displayed image is obtained by assigning a value, for instance a grey tone or a color, to each pixel. The grey tone or color of each pixel is determined by the properties of the signal vector associated with its respective voxel in the region of interest. In an ideal case, all voxels which represent the same physical characteristic of the object, for example, a particular type of tissue in medical imaging, should be associated with the same point in signal space. However, imaging devices are not ideal and various sources of noise result in the same type of tissue being associated with a distribution of signal vectors in signal space. Additionally, two different types of tissue, for example grey matter brain tissue and white matter brain tissue, may have signal vectors which are very similar. Thus, one of the key objectives in imaging technology is to characterize every significant domain in the region of interest (also referred to as "ROI") to be imaged so that distinct domains are distinguished in the displayed image, even if their respective signal characteristics are similar.
This problem of characterization of a specific subregion is rendered even more difficult by the presence of noise in the signal. Two types of noise are present in most signals: electronic noise and biological noise. The effects and properties of electronic noise are well understood and standard techniques have been developed to deal with it in imaging. The electronic noise is usually considered to be a random variable. As subregions of the region of interest are represented by a multi-dimensional distribution within the signal space, it may occur that those distributions for various subregions may overlap. This creates a problem in the identification of a grid pattern for a digitized subregion insofar as two subregions having similar characteristics may not be sufficiently contrasted in the final output image.
Various imaging techniques have been proposed to enhance contrast and circumvent the problem set forth above. The methods known to date for displaying image corresponding to certain signal characteristics fall into two major categories. In a first approach, the image is partitioned into a finite set of segments. This method, known as image segmentation, has been extensively used. In a second method, known as continuous grey-scale imaging, a grey value is assigned to each pixel in accordance with the intensity of the signal vector. Both of these techniques have various drawbacks that will now be briefly discussed.
The objective of the segmentation method is to group together voxels and produce an image by assigning a color to each of these groups. In a proposed segmentation method, the signal data are clustered into groups with similar signal characteristics. A distinct uniform color is then assigned to each of the clusters having the same signal characteristics. Recently, there has been an increased interest in a data clustering algorithm called fuzzy c-means clustering. By definition, a fuzzy set U is a function from a subset of R.sup.p into the interval [0,1] which assigns to each element of the subset X a grade of membership. The membership function is a function valued between zero and one and is a key concept of fuzzy sets. In this method, a signal vector having p components in the signal space is assigned to each of the voxels. The values of the components of the vector are the pixel intensities of the acquired images. The calculation of the membership function determining to which cluster a particular voxel belongs requires the definition of a distance metric. Typically, this distance metric is chosen to be the simple Euclidean distance in the signal space. The clustering begins by then randomly choosing a set of c-cluster centers v.sub.i within the signal space and defining a membership function u.sub.ik which would give the membership grade for the pixel k being a member of the fuzzy cluster i. Cluster centers are thereby redefined, and the procedure is iterated until the movement of cluster centers is made as small as possible. Pixels are assigned to clusters based on which of the c-membership functions is largest. One drawback of this algorithm is that the number of c clusters is arbitrarily chosen. Typically, the number of clusters is deliberately chosen to be higher than the expected number of individual subregion types.
Several methods are of interest to implement this algorithm. A first method called hierarchical processing using pyramid algorithms has turned out to be a valuable method because it allows the image to be examined at several levels of resolution at one time. The person skilled in the art will be able to find a thorough description of such a method in the following article: "Tissue Type Identification by MRI Using Pyramidal Segmentation and Intrinsic Parameters," Ortendhal Douglas, et al., Proceeding of the Ninth International Conference on Information Processing in Medical Imaging, Washington, D.C. (1985). In a second method, shape descriptors are used for identifying regions of suspected partial volume averaging. In a third method, histogram analysis can also be advantageously used as a form of gray level statistics. In this histogram method, the signal values are plotted in histograms according to their frequency of occurrence. However, in this histogram equalization method, the voxels are first assigned a gray level value which is then plotted in a histogram according to the frequency of occurrence. Such a histogram is therefore referred to as a gray level histogram. A summary of these segmentation methods can be found in: Ortendhal D.A., et al, MRI Image Segmentation Using Fuzzy Set Clustering and Spatial Correlations. "Book of Abstracts", Society of Magnetic Resonance in Medicine, 6th Annual Meeting, Aug. 17-21, 1987; and in Sklansky J., et al: Image Segmentation and Feature Extraction, IEEE Transactions on Systems, Man and Cybernetics, Vol. SMC-8, No. 4, Apr. 1978. In another proposed segmentation method, a boundary is drawn in the image whenever signal variation between two neighboring voxels is greater than a preset threshold. The drawback of this segmentation method still resides in the arbitrariness of the selection of the threshold. Numerous other ways of partitioning the image have also been proposed without resolving the inherent problems entailed by segmentation of an image.
The main disadvantage of the segmentation method remains in the arbitrariness of the clustering of the image, irrespective of the technique used to perform the segmentation itself (fuzzy set, threshold,...). More specifically, in the clustering algorithm, there is no way of determining what number of clusters should be used for partitioning the region of interest to be imaged. This also applies to the choice of the threshold. Since the threshold value or the number of clusters is arbitrary and the color assignment discontinuous, errors in the color segmentation are likely to occur. In particular, voxels of distinct domains having similar signal values may be represented by the same color. Several patents make use of the segmentation method or a refinement thereof.
Reference is first made to the Watanabe patent, U.S. Pat. No. 3,805,239. In the Watanabe patent, there is disclosed an apparatus comprising a memory device for storing in matrix format electrical signals corresponding to the gray levels of the respective picture elements of a pattern. In this apparatus, the differences between gray levels of a central picture element and of eight surrounding picture elements are determined in order to obtain some of the differences between the central picture element and the surrounding picture elements. These differential sums are then added up for each matrix containing a given picture element. After completing such additions with respect to numerous matrices in which different picture elements constitute the central one, the gray level of the picture element taken as the central one and which gives a maximum value from among the totals of differential sums thus computed is then detected. There is also provided a device for reading out of the memory device data on a prescribed gray level higher or lower than the gray level of maximum value which is used as a threshold value.
Another patent, U.S. Pat. No. 4,340,911 to Kato also uses the segmentation method. In this patent, the densities of three different tissues are plotted in a histogram. The three peaks corresponding to the frequency distribution of those three tissues are used to determine the threshold values necessary to produce the desired gradation of the image. Boundary levels are then determined to perform the gradation processing. Contrast between two tissues can be raised by lowering the level of the minimum density of the image corresponding to one of the tissues, down to the level of the fog density of the image.
The patent to Toraichi (U.S. Pat. No. 4,538,227) also uses the segmentation technique. In the Toraichi patent, the image processor obtains information about an organ to be imaged such as the boundary diagram, the volume, the centroid movement view and a three-dimensional view. The gray level values of given X-ray projections are plotted in a histogram. The extraction of the image boundary from the provided processed image is thus accomplished by segmenting a given image into a plurality of small regions, forming the small regions into ternary coded signals in comparison with thresholds K.sub.1 and K.sub.2 which are determined by the histogram of the gray scale of the gray level values.
Another approach to image processing consists in assigning a gray scale value to each of the pixels mapping into the voxels of the region of interest, whereby the intensity of the gray value is a function of the signals emitted by the voxels. This imaging technique, referred to as continuous gray scale imaging, is widely used. The basics of this method will now be briefly summarized.
A gray scale is by definition a one-dimensional real number line. To each voxel in the image, there is assigned a real value corresponding to a gray scale value. Actually, the grey scale is a discrete set of grey tones, but the assumption that the grey scale is a continuous scale is legitimate to a first approximation. As the signal space is typically a multi-dimensional space and the gray scale value a one-dimensional space, the mapping from the signal space into the gray scale real number line is necessarily not homomorphic. Projections from the signal space into the gray real number line are typically used to perform the grey value assignment.
In the projection method, a gray scale value is assigned to each pixel corresponding to the value of the signal vector projected onto a preselected axis, usually a coordinate axis. When a coordinate axis is chosen as a projection axis, the projection technique amounts to projecting the signal vector onto one of the signal basis vectors, and then assigning a gray scale value corresponding to the amplitude of this projection on the projection axis. A voxel is thus associated with a scalar which is associated to a particular gray value. In most current projection techniques, this projection is performed without further modulation by the mapping between the region of interest and the signal space. The projection method yields satisfactory images of distinct domains which are also spatially disjoint. However, such a method fails to discriminate between neighboring regions having similar signal values and spatially close to one another. The output image exhibits "poor contrast".
The concept of contrast is essential in image processing and is defined as the difference in the gray scale values assigned to two distinct voxels. In the projection method, the contrast is therefore dependent upon the distance between the two points in the signal space to which the two voxels are initially mapped. Thus, if the two voxels that are mapped have similar characteristics, more specifically, if the values of the projections of their corresponding signal vectors are nearly equal, the distance on the projection axis in the signal space between the two mapped voxels will be small. As the contrast depends on the difference between the two gray scale values, two voxels having similar signal characteristics are poorly contrasted in the projection method. To enhance the contrast between two subregions which map to nearby points in the signal space in a particular imaging technology, it becomes necessary to resort to other imaging technologies (e.g. use of pharmacological agents, etc).
The following example, taken from Nuclear Magnetic Resonance Imaging, clearly illustrates the foregoing analysis. In NMR imaging, three parameters are associated to each voxel. Three projections can thus be envisioned, corresponding to each of the coordinate axes and leading to three images. In each of these images, every voxel on each of the axes T.sub.1, T.sub.2 (spin-lattice relaxation and spin-spin relaxation time, respectively) and the proton density .rho. is assigned a gray scale value. The first image is a representation of the region of interest mapped according to the first type of relaxation T.sub.1. Two voxels having different times of relaxation T.sub.1 are therefore represented by two different gray values. This also applies to the second image produced in accordance with the second coordinate, T.sub.2, and the third image obtained from the proton density .rho. (the "proton image"). As discussed above, the contrast between neighboring voxels having similar signal characteristics is poor as the contrast depends on the distance chosen in the signal space. Furthermore, the analysis of three images requires special skills as the user is required to synthesize three types of images in order to draw conclusions for a diagnosis. In order to facilitate the reading of those images, a method has been disclosed entitled Hybrid Color MR Imaging Display and disclosed in the article: Weiss, et al. "Hybrid Color MR Imaging Display," AJR: 149: October 1987. In this method, two images are synthesized into one image. A two-dimensional resolvable contrast scale uses the pixel intensity from one image and the pixel luminance of the other image. The pixel intensities from one image are assigned varying special hues whereas the luminance of these hues is derived from the intensities of the corresponding pixels of the second specially aligned image. This technique, however, does not produce a sharp contrast between neighboring voxels of similar intensities but made of different subregions.
It should be noted that in the imaging techniques proposed so far, smoothing operations are used to diminish spurious effects that may be present in the digital image as a result of a poor sampling system or transmission channel. In other words, these techniques already assume that a gray level image has been obtained by projecting or by segmenting the region to be processed in accordance with the signal characteristics of the other voxels.